A Simple Tricky Example

Suppose we have:

• two sets of facts, {fact1, fact2} and {fact3, fact4}, among others
• two tests s and t, with the following rules, plus possibly others which don't involve these facts or test results:

	s-result1 IF fact1 
     s-result1 IF fact3 
     ... 
     t-result1 IF fact1
     t-result1 IF fact4
     ... 

Now assume that the student gets s-result1 and t-result1, and the question is "Is fact2 consistent with those results?"

Since fact2 doesn't predict any results, it can't be ruled out directly by any result that does or doesn't occur. And yet fact2 is, in fact, provably inconsistent with the above results. Why? Because

• If s-result1 and t-result1 are both true, then fact1 OR fact3 and fact1 OR fact4 are both true.
• fact3 and fact4 can't both be true, therefore one has to be false.
• Making either one false means fact1 has to be true.
• fact1 and fact2 can't both be true, so fact2 has to be false.

Hence, even if the rules were constrained to single causes, which they weren't, you would still need something equivalent to a propositional theorem prover.

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